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Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution function

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Usábel Rodrigo, Miguel Arturo (1998) Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution function. [ Documentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales; nº 02, 1998, ISSN: 2255-5471 ]

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Official URL: http://eprints.ucm.es/27083/




Abstract

The non-ruin probability, for initial reserves u, in the classical can be calculated using the so-called Bromwich-Mellin inversion formula, an outstanding result from Residues Theory first introduced for these purposes by Seal(1977) for exponential claim size. We will use this technique when claim sizes follow a generalized r-convolution function distribution. Some of the most frequently used heavy-tailed distributions in actuarial science belongs to this family. Thorin(1977) or Berg(1981) proved that Pareto distributions are members of this family; so Thorin(1977) did with Log-normal distributions.


Item Type:Working Paper or Technical Report
Uncontrolled Keywords:Ultimate non-ruin probability; Laplace transforms; Bromwich-Mellin inversion formula; Gerenalized r-convolution functions.
Subjects:Sciences > Mathematics > Probabilities
Series Name:Documentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales
Volume:1998
Number:02
ID Code:27083
Deposited On:13 Oct 2014 17:31
Last Modified:03 Sep 2015 12:05

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